Re: Expanding Trig Power Identities
- To: mathgroup at smc.vnet.net
- Subject: [mg30365] Re: [mg30348] Expanding Trig Power Identities
- From: BobHanlon at aol.com
- Date: Sun, 12 Aug 2001 02:29:53 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/8/11 3:59:50 AM, adam_jurhs at xontech.com writes:
>How can I use Mathematica to find the expansion of various trigonometric
>power
>identities? I've already tried TrigExpand w/o succes.
>
>I have functions of the form Sin[a](Sin[b])^n and Cos[a](Cos[b])^n
>where n is a power.
>
>I would like to get the fully expanded version of these functions, so
>that there are no more powers involved. If n=1 then the answer is
>just the standard product relations that you can look up in the back
>of any trig book. But I need to be able to do it for higher powers of
>n. And I don't know how to even do it for n=1.
>
TrigReduce[Sin[a]*Sin[b]^3]
(1/8)*(-Cos[a - 3*b] + 3*Cos[a - b] - 3*Cos[a + b] +
Cos[a + 3*b])
Table[{y = Sin[a]*Sin[b]^n, "=", TrigReduce[y]}, {n, 4}] // TableForm
Table[{y = Cos[a]*Cos[b]^n, "=", TrigReduce[y]}, {n, 4}] // TableForm
Bob Hanlon
Chantilly, VA USA